Sprinkle steak with salt and pepper. Cook steak in a skillet over medium-high heat until well browned, about 1 minute per side. Reduce heat; add half the butter and cook 3 to 5 minutes on each side. Remove the meat from the pan and keep warm.
Drain fat from pan; add green onions and wine. Bring to a boil and whisk in garlic, scraping up the browned bits from the pan. Boil until wine is reduced by half; remove from heat and stir in remaining butter.
Slice meat against the grain into thin strips. Serve over noodles, spooning sauce on top.
Servings: 4